Fundamental Algebraic Geometry

seminar at MIMUW, academic year 2013/2014

summer semester: Thursdays, 8:30-10:00, room 1780, Banacha 2

winter semester: Wednedays, 14:15-15:45, room 1780, Banacha 2

Official page

• FGA: Fantechi et al, FGA explained

• EH: Eisenbud and Harris, The Geometry of Schemes
• HA: Hartshorne, Deformation Theory
• KO: Koll\'ar, Rational curves on algebraic varieties
• Mum: Mumford, Lectures on curves on algebraic varieties
• SE: Sernesi, Deformations of algebraic schemes

1. Winter semester
2. Oct. 16: FGA 5.1 explained by Joachim Jelisiejew: definitions and representability of the Grassmannian functor (EH).
3. Oct. 23, FGA 5.2 explained by Piotr Pokora: Castelnuovo-Mumford regularity (Mum).
4. Oct. 30, FGA 5.3 explained by Łukasz Sienkiewicz: semicontinuity and Grothendieck complex.
5. Nov. 6, FGA 5.3 explained by Łukasz Sienkiewicz continued.
6. Nov. 13, FGA 5.4 explained by Maciej Zdanowicz: flattening stratification.
7. Nov. 27, FGA 5.5 explained by Maksymilian Grab: representability of $Quot$, part I.
8. Dec. 4, FGA 5.5 explained by Maksymilian Grab: representability of $Quot$, part II.
9. Dec. 18, FGA 5.5 explained by Maksymilian Grab: representability of $Quot$, part III.
10. Jan. 8, FGA 5.6.2 explained by Maciej Zdanowicz: schemes of morphisms.
11. Jan. 15, FGA 6 explained by Joachim Jelisiejew: tangent space to $Hilb$.
12. Jan. 15, FGA 6 explained by Joachim Jelisiejew: tangent-obstruction theory for $Hilb$ and consequences for the dimension of the Hilbert scheme (FGA 6.4.11).
13. Summer semester
14. Mar. 03, FGA 6.4.11 explained by Adam Michalik: Schemes parametrising morphisms and their tangent spaces (SE), functors $T_0$, $T_1$, $T_2$ (HA 1.3).
15. Mar. 10. No meeting.
16. Mar. 17: Adam Michalik: properties of $T_i$ and infinitesimal lifting property (Ha 1.3, 1.4).
17. Mar. 24: Adam Michalik: deformations of rings (Ha 1.5).
18. Mar. 31: problem solving: exercises from chapter 1 of HA.
19. Apr. 3: problem solving continued.
20. Apr. 10: problem solving continued.
21. Apr. 24: problem solving continued: Hilbert scheme of hypersurfaces.
22. May 8: presentation of PhD project --- Łukasz Sienkiewicz.
23. May 15: presentation of PhD project --- Łukasz Sienkiewicz, continued.
24. May 22: presentation of PhD project --- Maciej Zdanowicz.
25. May 29: presentation of PhD project --- Joachim Jelisiejew.
26. July 5: presentation of PhD project --- Maksymilian Grab.